What Mahmoud Abbas said last week was that he’d like to visit his hometown, not live there. But because that hometown — the picturesque Galilee city of Safed — is in what’s today Israel, and because, as leader of the Palestine Liberation Organization, Abbas represents the people who claim the same land, his words were taken as more than a rumination on possible vacation plans. He had punctured the seal on the biggest can of worms in the Israeli-Palestinian conflict, the “right of return.”

Abbas, 77, left Safed when he was 13, his family joining the torrent of Arab families who fled their homes in 1948 ahead of advancing Jewish forces who were intent on creating Israel. Some 700,000 Arab residents departed, many at gunpoint, taking refuge across international borders in Syria, Lebanon, Jordan and the Gaza Strip, which was then administered by Egypt. Most expected to come back, once Arab states got their act together and finally defeated the Jews on the battlefield. It never happened. What victories came their way were in the realm of diplomacy and rhetoric: in December 1948 a sympathetic U.N. passed a resolution, Resolution 194, saying they should be allowed to go back to their homes. Even more importantly, a couple of decades later militants led by Yasser Arafat forged the Palestinian national identity around the demand.

To leaders trying to negotiate an end to the conflict, the challenge is reconciling the rhetoric of righteousness with the reality that has taken hold over 64 years. Over that time, the world has nurtured the dream of “return.” Syria and Lebanon sequestered the refugees in camps, ostensibly because they were going back. The U.N. made the legal status of refugee something that can be inherited: today it classifies more than 6.6 million Palestinians as refugees. At the same time, the fact of Israel became more and more concrete — literally, so. Almost none of the homes the Palestinians fled still exist.

“In 1973, my father’s house was still around,” says Jamal Ebeid, leaning on the counter of his falafel shop in the Jenin refugee camp, where he was born 56 years ago. His parents lived on the Mediterranean coast, 30 miles (50 km) away in the city of Haifa. “But we went to visit in ’76, and it was gone.” Ebeid shrugs, but not dismissively. The subject is painful. “Everybody has a spot in his heart for his land,” he says.

In the camps, the romance of the remembered can live on nearly as vividly today as it did to the refugees David Grossman visited for his extraordinary book, The Yellow Wind. “Growing our crops there is different than growing our crops here,” Bassam Abed Rabo, 53, a handyman in Ramallah’s al-Amari camp, tells TIME. “Apples, sabra, even the eggs the chickens lay taste better there, in that soil.” The anguish is worsened by the dissonance of Palestinian political orthodoxy, which prefers to deny the obvious reality, at least publicly. In the 1970s, a Palestinian academic was interviewing refugees in Syria. He asked Arafat for permission to ask people whether they still wanted to go back to their homes. Arafat forbade the question. “May I remind you,” the academic quoted Arafat as saying, “that our movement is based on three words: right of return.”

But in 2003 another researcher managed to broach the subject, interviewing 4,500 refugees in Jordan, Lebanon, Gaza and the West Bank. Only 10% said they would live in Israel if given the option, while 54% opted for monetary compensation and a home on the West Bank or Gaza. The other third said they would prefer to live in other countries, or rejected the terms described. Monetary compensation is, in fact, one of the options offered to refugees under U.N. Resolution 194, but Palestinian leaders say they dare not point this out it in speeches. For ignoring the taboo, a mob attacked the Ramallah office of the pollster, Khalil Shikaki, the respected director of the Palestinian Center for Policy and Survey Research.

So Abbas’ remarks last week, which were broadcast in an interview with an Israeli television station, were hailed as “courageous” by Israeli President Shimon Peres and other Israelis eager for a resumption in peace talks. They understood the statement was intended to reassure anxious Israelis that Palestinians will be content with Israeli troops pulling out of the West Bank and Gaza, and will not later push to reverse the losses of 1948. Prime Minister Benjamin Netanyahu dismissed Abbas’ remarks as insincere.

The reaction among Palestinians was harsh. Abbas was vilified by Hamas, the Islamist group that governs Gaza, as well as by moderates who thought he had ceded a major principle, which Abbas denied. In an interview with TIME last year, the Palestinian Authority President discussed both the practicality and potency of “return.” “You know it is a magic word,” Abbas told me, “and everybody looks to return back, to see his home, to see his land, to see the rest of his family if there is [any]. So everybody is waiting for right of return. According to the Arab Peace Initiative, we found a solution that this issue should be dealt in this way; that we will find a just and agreed upon solution with the Israelis, according to U.N. Resolution 194. Which means that some people will return — without affecting the fabric of the Israelis of course.”

“If we tell them, O.K., we will send 5 million Palestinians, everything will be destroyed in Israel. We don’t want to destroy Israel of course, we want to live with Israel. But we want to give the right for some numbers to return back, which will not affect the social fabric.” What’s that fabric now? Abbas noted that Israel’s population of 8 million people currently includes 1.6 million Palestinians, sometimes called Israeli Arabs, being descendants of those who were allowed to remain in 1948. There are also several hundred thousand Russian immigrants who are not Jewish. “So now you have 2 million, but it doesn’t affect the nature of Israel,” Abbas says.

How many Palestinian refugees would want to return?

“I don’t know,” Abbas said. “I don’t argue with anybody. ‘O.K., you want your right of return? It’s O.K., when we come to it, we will do our best to try to fulfill your dreams. According to the Arab Peace Initiative.’ But at that time, I don’t know whether the 5 million will ask — maybe some of them will ask for compensation and that’s it. Some of them will ask, ‘O.K., I will return back to Palestine.’ Some will return back to Israel. But when they think of it deeply — ‘O.K., you are going to Israel, to be a member of the Israeli society, to raise the Israeli flag, to have the identity card of Israel, to have an Israeli passport?’ ‘Oh, no no.’ We don’t go into details, no, but if somebody asks, I will answer them: ‘If you want to go to Israel, of course, you have to be an Israeli citizen. You have to make salute to their national anthem.’ ‘Oh, no no no!’ Some say, ‘Yes, I will go. I need to go.’”

When negotiations were still going on, Palestinian and Israeli officials bandied numbers in the low thousands when addressing the number of refugees who would be allowed back. One of the murkiest questions awaiting any potential deal is what the perhaps 2 out of 3 Palestinians who regard themselves as refugees would make of such a figure. “The right of return is a demand, and only a demand,” says Bilal Shalabi, 31, also born in the Jenin camp, where his family arrived from Zareen, a few miles north. The distinction recognizes the negotiating value of the right in right of return, something far more easily used as leverage than a real-world option. “Who is going to be able to achieve the right of return for the Palestinians?” Shalabi says. “Who’s going to achieve it? Everybody knows this. All the people know this. Everybody knows this.”

Karl Vick has been TIME's Jerusalem bureau chief since 2010, covering Israel,the Palestine territories and nearby sovereignties. He worked 16 years at the Washington Post in Nairobi, Istanbul, Baghdad, Los Angeles and Rockville, MD.